0.050505… as a Fraction

0.050505… (0.05 repeating) as a fraction is 5/99.

How to convert 0.050505… to a fraction

  1. Let x = 0.050505... (the underlined part, 05, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 5.050505...
  3. Subtract to cancel the repeating tail: 100x − x = 5 − 0, so 99x = 5.
  4. Solve: x = 5/99. The greatest common divisor is 1, so x = 5/99 (already in lowest terms).

Check

Divide 5 by 99 on a calculator: 5 ÷ 99 = 0.0505050505… which matches 0.050505….

Similar repeating decimals

DecimalFraction
0.0333…1/30
0.037037037…1/27
0.040404…4/99
0.0444…2/45
0.054054054…2/37
0.0555…1/18
0.060606…2/33
0.0666…1/15

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.